Dampers of this kind are known through prior use and are used for example for damping driver's seats in lorries or tractors. It is also possible in principle to use dampers of this kind as chassis dampers. In addition, it is possible to equip sports equipment and in particular rowing machines and the like with such dampers. Dampers of this kind are also known as twin-tube dampers. These kinds of dampers can vary in their damping behavior depending on the direction in which the damper is activated. For example a small damping effect may be desirable when the damper is activated in insertion direction, i.e. when a driver's seat is loaded. In comparison a large damping effect may be desirable in an extraction direction opposite the insertion direction, i.e. when the pressure is lifted from the driver's seat again. In twin-tube dampers when a piston rod is inserted pressure fluid, such as for example oil, is displaced from an inner working chamber and flows through a piston rod guide losing as little pressure as possible into an outer equalizing chamber. When the piston rod is drawn out the oil flow in the piston rod guide is opposed by a resistance, in order to achieve the increased damping effect. From prior use a valve arranged in the piston rod guide is known which opens with the piston rod pushed in and allows oil to flow through the piston rod guide with no resistance. Upon extraction the piston rod guide is sealed hermetically by the valve. If the valve is not functioning correctly the oil flow can be prevented when the piston rod is pushed in so that a surprisingly high damping effect is achieved. This is perceived for example as blocking the damper. It is also known from known prior use to use an annular gap provided between the piston rod and the piston rod guide as a flow passage for the pressure fluid. The size of the annular gap and thereby the damping effect of the damper overall are directly dependent on the manufacturing tolerances of the piston rod and the piston rod guide. Even small variations in the dimensions can significantly change the damping effect.